Abstract

A crystalline dislocation-density formulation that was incorporated with a nonlinear finite-element (FE) method was utilized to understand and to predict the thermomechanical behavior of an hexagonal closest packed (h.c.p.) zircaloy system with hydrides with either face-centered cubic (f.c.c.) or body-centered cubic (b.c.c.) hydrides. This formulation was then used with a recently developed fracture methodology that is adapted for finite inelastic strains and multiphase crystalline systems to understand how different microstructurally based fracture modes nucleate and propagate. The interrelated microstructural characteristics of the different crystalline hydride and matrix phases with the necessary orientation relationships (ORs) have been represented, such that a detailed physical understanding of fracture nucleation and propagation can be predicted for the simultaneous thermomechanical failure modes of hydride populations and the matrix. The effects of volume fraction, morphology, crystalline structure, and orientation and distribution of the hydrides on simultaneous and multiple fracture modes were investigated for radial, circumferential, and mixed distributions. Another key aspect was accounting for temperatures changes due to the effects of thermal conduction and dissipated plastic work and their collective effects on fracture. For hydrided aggregates subjected to high temperatures, thermal softening resulted in higher ductility due to increased dislocation-density activity, which led to higher shear strain accumulation and inhibited crack nucleation and growth. The predictions provide validated insights into why circumferential hydrides are more fracture-resistant than radial hydrides for different volume fractions and thermomechanical loading conditions.

References

1.
Northwood
,
D. O.
,
1985
, “
The Development and Applications of Zirconium Alloys
,”
Mater. Desi.
,
6
(
2
), pp.
58
70
.
2.
Mishima
,
Y.
, and
Okubo
,
T.
,
1972
, “
Effect of Thermal Cycling on the Stress Orientation and Circumferential Ductility in Zircaloy-2
,”
Can. Metall. Q.
,
11
(
1
), pp.
157
164
.
3.
Wallace
,
A.
,
Shek
,
G.
, and
Lepik
,
O.
,
2008
, “
Effects of Hydride Morphology on Zr-2.5Nb Fracture Toughness
,”
Zirconium in the Nuclear Industry: Eighth International Symposium
,
ASTEM Special Technical Publications, ASTM International
.
4.
Fearnehough
,
G. D.
, and
Cowan
,
A.
,
1967
, “
The Effect of Hydrogen and Strain Rate on the ‘Ductile-Brittle’ Behaviour of Zircaloy
,”
J. Nucl. Mater.
,
22
(
2
), pp.
137
147
.
5.
Mouton
,
I.
,
Breen
,
A. J.
,
Wang
,
S.
,
Chang
,
Y.
,
Szczepaniaka
,
A.
,
Kontis
,
P.
,
Stephensona
,
L. T.
,
Raabe
,
D.
,
Herbig
,
M.
,
Britton
,
T. B.
, and
Gaulta
,
B.
,
2019
, “
Quantification Challenges for Atom Probe Tomography of Hydrogen and Deuterium in Zircaloy-4
,”
Micros. Microanal.
,
25
(
2
), pp.
481
488
.
6.
Bradbrook
,
J. S.
,
Lorimer
,
G. W.
, and
Ridley
,
N.
,
1972
, “
The Precipitation of Zirconium Hydride in Zirconium and Zircaloy-2
,”
J. Nucl. Mater.
,
42
(
2
), pp.
142
160
.
7.
Hong
,
S. I.
,
Lee
,
K. W.
, and
Kim
,
K. T.
,
2002
, “
Effect of the Circumferential Hydrides on the Deformation and Fracture of Zircaloy Cladding Tubes
,”
J. Nucl. Mater.
,
303
(
2–3
), pp.
169
176
.
8.
Billone
,
M. C.
,
Burtseva
,
T. A.
, and
Einziger
,
R. E.
,
2013
, “
Ductile-to-Brittle Transition Temperature for High-Burnup Cladding Alloys Exposed to Simulated Drying-Storage Conditions
,”
J. Nucl. Mater.
,
433
(
1–3
), pp.
431
448
.
9.
Birch
,
R.
,
Wang
,
S.
,
Tong
,
V.
, and
Britton
,
B.
,
2018
, “
Short Communication: The Effect of Cooling Rate and Grain Size on Hydride Microstructure in Zircaloy-4
,”
arXiv
,
513
, pp.
221
225
.
10.
Leitch
,
B. W.
, and
Puls
,
M. P.
,
1992
, “
Finite Element Calculations of the Accommodation Energy of a Misfitting Precipitate in an Elastic-Plastic Matrix
,”
Metall. Trans. A
,
23
(
3
), pp.
797
806
.
11.
Motta
,
A. T.
,
Capolungo
,
L.
,
Chen
,
L. Q.
,
Cinbiz
,
M. N.
,
Daymond
,
M. R.
,
Koss
,
D. A.
,
Lacroix
,
E.
,
Pastore
,
G.
,
Simon
,
P. C. A.
,
Tonks
,
M. R.
,
Wirth
,
B. D.
, and
Zikry
,
M. A.
,
2019
, “
Hydrogen in Zirconium Alloys: A Review
,”
J. Nucl. Mater.
,
518
, pp.
440
460
.
12.
Ashmawi
,
W. M.
, and
Zikry
,
M. A.
,
2002
, “
Prediction of Grain-Boundary Interfacial Mechanisms in Polycrystalline Materials
,”
ASME J. Eng. Mater. Technol.
,
124
(
1
), pp.
88
96
.
13.
Shanthraj
,
P.
, and
Zikry
,
M. A.
,
2011
, “
Dislocation Density Evolution and Interactions in Crystalline Materials
,”
Acta Mater.
,
59
(
20
), pp.
7695
7702
.
14.
Kubin
,
L.
,
Devincre
,
B.
, and
Hoc
,
T.
,
2008
, “
Modeling Dislocation Storage Rates and Mean Free Paths in Face-Centered Cubic Crystals
,”
Acta Mater.
,
56
(
20
), pp.
6040
6049
.
15.
Kim
,
J.-S.-S.
,
Kim
,
T.-H.-H.
,
Kook
,
D.-H.-H.
, and
Kim
,
Y.-S.-S.
,
2015
, “
Effects of Hydride Morphology on the Embrittlement of Zircaloy-4 Cladding
,”
J. Nucl. Mater.
,
456
, pp.
235
245
.
16.
Chan
,
H.
,
Roberts
,
S. G.
, and
Gong
,
J.
,
2016
, “
Micro-scale Fracture Experiments on Zirconium Hydrides and Phase Boundaries
,”
J. Nucl. Mater.
,
475
, pp.
105
112
.
17.
Gu
,
X. F.
, and
Zhang
,
W. Z.
,
2014
, “
A Simple Method for Calculating the Possible Habit Planes Containing One Set of Dislocations and Its Applications to Fcc/Bct and Hcp/Bcc Systems
,”
Metall. Mater. Trans. A
,
45
(
4
), pp.
1855
1865
.
18.
Motta
,
A. T.
,
Yilmazbayhan
,
A.
,
da Silva
,
M. J. G.
,
Comstock
,
R. J.
,
Was
,
G. S.
,
Busby
,
J. T.
,
Gartner
,
E.
,
Peng
,
Q.
,
Jeong
,
Y. H.
, and
Park
,
J. Y.
,
2007
, “
Zirconium Alloys for Supercritical Water Reactor Applications: Challenges and Possibilities
,”
J. Nucl. Mater.
,
371
(
1–3
), pp.
61
75
.
19.
Porter
,
D. A.
, and
Easterling
,
K. E.
,
2009
,
Phase Transformations in Metals and Alloys
, (revised reprint), 3rd ed.,
CRC Press
,
Boca Raton, FL
.
20.
Mohamed
,
I.
, and
Zikry
,
M. A.
,
2021
, “
Modeling of the Microstructural Behavior of Hydrided Zirconium Alloys
,”
Comput. Mech.
21.
Ziaei
,
S.
,
Wu
,
Q.
, and
Zikry
,
M. A.
,
2015
, “
Orientation Relationships Between Coherent Interfaces in Hcp-Fcc Systems Subjected to High Strain-Rate Deformation and Fracture Modes
,”
J. Mater. Res.
,
30
(
15
), pp.
2348
2359
.
22.
Kubo
,
T.
,
Wakashima
,
Y.
,
Amano
,
K.
, and
Nagai
,
M.
,
1985
, “
Effects of Crystallographic Orientation on Plastic Deformation and SCC Initiation of Zirconium Alloys
,”
J. Nucl. Mater.
,
132
(
1
), pp.
1
9
.
23.
Musienko
,
A.
, and
Cailletaud
,
G.
,
2009
, “
Simulation of Inter- and Transgranular Crack Propagation in Polycrystalline Aggregates Due to Stress Corrosion Cracking
,”
Acta Mater.
,
57
(
13
), pp.
3840
3855
.
24.
Pouillier
,
E.
,
Gourgues
,
A. F.
,
Tanguy
,
D.
, and
Busso
,
E. P.
,
2012
, “
A Study of Intergranular Fracture in an Aluminium Alloy Due to Hydrogen Embrittlement
,”
Int. J. Plast.
,
34
, pp.
139
153
.
25.
Hansbo
,
A.
, and
Hansbo
,
P.
,
2004
, “
A Finite Element Method for the Simulation of Strong and Weak Discontinuities in Solid Mechanics
,”
Comput. Meth. Appl. Mech. Eng.
,
193
(
33–35
), pp.
3523
3540
.
26.
Wu
,
Q.
, and
Zikry
,
M. A.
,
2014
, “
Microstructural Modeling of Crack Nucleation and Propagation in High Strength Martensitic Steels
,”
Int. J. Solids Struct.
,
51
(
25–26
), pp.
4345
4356
.
27.
Morris
,
J. W.
,
2011
, “
On the Ductile-Brittle Transition in Lath Martensitic Steel
,”
ISIJ Int.
,
51
(
10
), pp.
1569
1575
.
28.
Zikry
,
M. A.
,
1994
, “
An Accurate and Stable Algorithm for High Strain-Rate Finite Strain Plasticity
,”
Comput. Struct.
,
50
(
3
), pp.
337
350
.
29.
Kubo
,
T.
,
Kobayashi
,
Y.
, and
Uchikoshi
,
H.
,
2013
, “
Determination of Fracture Strength of δ-Zirconium Hydrides Embedded in Zirconium Matrix at High Temperatures
,”
J. Nucl. Mater.
,
435
(
1–3
), pp.
222
230
.
30.
Oono
,
N.
,
Kasada
,
R.
,
Higuchi
,
T.
,
Sakamoto
,
K.
,
Nakatsuka
,
M.
,
Hasegawa
,
A.
,
Kondo
,
S.
,
Iwata
,
N. Y.
,
Matsui
,
H.
, and
Kimura
,
A.
,
2013
, “
Comparison of Irradiation Hardening and Microstructure Evolution in Ion-Irradiated Delta and Epsilon Hydrides
,”
J. Nucl. Mater.
,
442
(
1–3
SUPPL.1), pp.
S826
S829
.
31.
Hong
,
S. I.
, and
Lee
,
K. W.
,
2005
, “
Stress-Induced Reorientation of Hydrides and Mechanical Properties of Zircaloy-4 Cladding Tubes
,”
J. Nucl. Mater.
,
340
(
2–3
), pp.
203
208
.
32.
Daum
,
R. S.
,
Majumdar
,
S.
,
Liu
,
Y.
, and
And Billone
,
M. C.
,
2006
, “
Radial-Hydride Embrittlement of High-Burnup Zircaloy-4 Fuel Cladding
,”
J. Nucl. Sci. Technol.
,
43
(
9
), pp.
1054
1067
.
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